Sparse Q-Learning: Offline Reinforcement Learning with Implicit Value Regularization

Most offline reinforcement learning (RL) methods suffer from the trade-off between improving the policy to surpass the behavior policy and constraining the policy to limit the deviation from the behavior policy as computing Q-values using out-of-distribution actions will suffer from errors due to distributional shift. The recent proposed \textit{In-sample Learning} paradigm (e.g., IQL), which improves the policy by quantile regression using only data samples, shows great promise because it learns an optimal policy without querying the value function of any unseen actions. However, it remains unclear how this type of method handles the distributional shift in learning the value function. In this work, we make a key finding that the in-sample learning paradigm arises under the \textit{Implicit Value Regularization} (IVR) framework. This gives a deeper understanding of why the in-sample learning paradigm works, i.e., it applies implicit value regularization to the policy. Based on the IVR framework, we further propose a practical algorithm, which uses the same value regularization as CQL, but in a complete in-sample manner. Compared with IQL, we find that our algorithm introduces sparsity in learning the value function, we thus dub our method Sparse Q-learning (SQL). We verify the effectiveness of SQL on D4RL benchmark datasets. We also show the benefits of sparsity by comparing SQL with IQL in noisy data regimes and show the robustness of in-sample learning by comparing SQL with CQL in small data regimes. Under all settings, SQL achieves better results and owns faster convergence compared to other baselines.